Soil Bearing Capacity Calculator

The Terzaghi equation, the foundation of geotechnical engineering

Karl Terzaghi, considered the father of modern geotechnical engineering, derived this equation in 1943 for predicting the load a soil can support before catastrophic failure. It’s been refined many times (Meyerhof, Hansen, Vesic) but the core form remains:

qu = c·Nc + γ·Df·Nq + 0.5·γ·B·Nγ

Where:

• qu: ultimate bearing capacity (kPa), the load that causes failure
• c: soil cohesion (kPa), the internal sticking-together strength
• γ: unit weight of soil (kN/m³)
• Df: foundation depth (m), how deep the footing sits below grade
• B: foundation width (m)
• Nc, Nq, Nγ: dimensionless bearing capacity factors (depend on φ, the internal friction angle)

The three terms represent three failure mechanisms:

1. c·Nc is cohesion resistance, which dominates in clays
2. γ·Df·Nq is overburden pressure, so a deeper footing gets more support
3. 0.5·γ·B·Nγ is friction along the failure wedges, which dominates in sands

Bearing capacity factors by friction angle

The factors Nc, Nq, and Nγ depend entirely on the internal friction angle φ:

For clays (φ ≈ 0), only the first term matters. For sands (c ≈ 0), only the second and third terms matter. Most real soils are somewhere in between.

Safety factor, the engineering convention

The ultimate capacity qu is the failure load. To get the safe (allowable) bearing capacity, divide by a factor of safety:

qs = qu / FS

Standard FS values:

FS = 3 means the safe load is 1/3 of the failure load, a 200% margin. This accounts for soil variability, construction tolerances, unknown loading conditions, and time-dependent effects (creep, consolidation).

Foundation shape corrections (Meyerhof, 1963)

The original Terzaghi formula was for strip footings (infinite length). Different shapes get correction factors:

So a square footing has 30% higher cohesion contribution but only 80% of the friction contribution of a strip footing. For most building columns (typically square or rectangular pad footings), the corrections matter.

Presumptive bearing values, and why they disagree with the formula

Every building code carries a table like this one. It lists a bearing pressure you are permitted to design to without any site investigation at all, purely on the basis of what the soil looks like in the trench.

Run the Terzaghi equation on the same soil and you will usually get a considerably larger number, often two or three times larger. Both are correct. They answer different questions.

The presumptive value assumes nobody measured anything, so it is deliberately pessimistic and absorbs the risk that the soil is worse than it looks. The Terzaghi result assumes that c, φ and γ really are the values you fed it, which is only true if somebody sampled the ground and tested it. Feed the equation a guess and you get a precisely calculated guess.

In practice: use the presumptive value for sketch design and for small buildings where nobody is going to pay for boreholes. Use a calculated capacity only when you have a geotechnical report to back the parameters, and expect an engineer to sign for it. The calculator above shows you both, side by side, for exactly this reason.

One place the gap becomes absurd is rock. Terzaghi was derived for soil that fails by shearing through a wedge, and intact rock does not behave that way at all. Ask the equation about sound rock and it will happily return tens of thousands of kPa. No code will let you use it, and the real limit is usually the compressive strength of your own concrete rather than anything in the ground.

Why building codes still mostly use the Terzaghi method

Modern soil mechanics has more sophisticated tools (finite element analysis, limit equilibrium with multiple failure surfaces). But for routine shallow foundation design, the Terzaghi equation is:

• Simple enough to compute by hand
• Well-validated against decades of foundation performance
• Conservative (errs on the safe side)
• Built into virtually every building code worldwide
• Familiar to every practicing geotechnical engineer

IBC, ASCE, BS 8004 and Eurocode 7 all incorporate the Terzaghi framework with their own modifications.

Common failure modes

Three ways a foundation can fail:

1. General shear failure. The soil shears in a wedge below the footing. Common in dense sand and stiff clay. Sudden and dramatic.
2. Local shear failure. Partial shearing without complete soil rupture. Common in medium-dense sand and medium-stiff clay. Gradual settlement under load.
3. Punching shear failure. The footing punches downward without horizontal soil movement. Common in loose sand. Slow downward movement under load.

Terzaghi originally derived his equation for general shear. For local and punching failure, modified factors are used (typically Nc/Nq/Nγ reduced by about 1/3).

Beyond bearing capacity: settlement

A foundation can pass bearing capacity check and still fail by excessive settlement. Most buildings tolerate 25 mm of total settlement (or 20 mm differential between adjacent footings) before structural cracking begins. Settlement calculations are separate from bearing capacity and often more restrictive. Many designs are settlement-limited, not capacity-limited.

For clays, settlement involves:

• Immediate settlement (elastic, within minutes)
• Primary consolidation (months to years, water squeezing out)
• Secondary compression (decades, creep)

For sands, settlement is almost entirely immediate (within hours of loading).

Site investigation matters more than the formula

The Terzaghi equation is only as good as the inputs. For real foundation design:

1. Soil sampling. Boreholes at 5-10 m spacing, samples from each strata
2. In-situ testing. Standard Penetration Test (SPT) blow counts, Cone Penetration Test (CPT)
3. Lab testing. Direct shear, triaxial, consolidation tests
4. Groundwater monitoring. It affects effective stress and capacity

A geotechnical investigation for a single-family home costs $2,000-$5,000; for a major commercial building, $25,000-$100,000+. Skipping it to save money is the #1 cause of foundation problems.

Worked example

A 2 m × 2 m square footing for a column carrying 800 kN, in stiff clay (c = 100 kPa, φ = 10°, γ = 18 kN/m³), at Df = 1.5 m depth:

• Nc = 8.35, Nq = 2.47, Nγ = 1.22
• Shape factors: sc = 1.3, sq = 1.2, sγ = 0.8
• qu = (100 × 8.35 × 1.3) + (18 × 1.5 × 2.47 × 1.2) + (0.5 × 18 × 2 × 1.22 × 0.8)
• qu = 1,086 + 80 + 17.6 = 1,184 kPa
• Safe capacity: qs = 1,184 / 3 = 395 kPa
• Pressure under footing: 800 / (2 × 2) = 200 kPa
• 200 < 395: footing is adequate ✓

Bottom line

The Terzaghi equation predicts ultimate bearing capacity from soil properties (cohesion, friction angle, density), foundation geometry, and depth. Apply a factor of safety of 3 for routine buildings. Real geotechnical engineering requires site investigation and engineering judgment. This calculator is for preliminary estimates, not final design. Always consult a licensed geotechnical engineer for actual construction.